1. Field of the Invention
This invention relates to digital filters and more particularly to such a filter in which the least significant (roundoff) bits of the quantizer are fed back for summation with the rounded bits to minimize roundoff noise.
2. Description of the Prior Art
The basic elements in the implementation of a digital filter are shown in FIG. 1 and comprise an adder 11, a unit delay circuit 12 which stores the value of a previous sampling sequence, a multiplier 13 to multiply the value of the previous sequence by a constant "a", and a quantizer 14 which quantizes the output of multiplier 13 and provides the quantized signal to adder 11 for summation with the digital input signal "u(n)" to be filtered. In this prior art filter, in view of the computational limitations of the computer circuitry, the least significant bits in the quantizer output (referred to as "roundoff" bits) are thrown away, the remaining bits which are utilized in the computation being referred to as "rounded" bits. This produces a significant error or "noise" in the output which significantly lessens the accuracy of the computation, particularly in situations where multiplications are performed on the signals thus compounding the errors. While this problem has been recognized for many years (see, for example, the discussing starting at the bottom of page 107 of "Digital Processing of Signals" by Gold and Rader, published by McGraw and Hill in 1969), no successful solution has been provided in the prior art. In addition to the aforementioned book by Gold and Rader, the following books on digital signal processing are pertinent for providing background information for the present application: "Theory and Application of Digital Signal Processing" by Rabiner and Gold, published by Prentiss-Hall Inc., 1975, and "Digital Signal Processing" by Oppenheim and Schafer, published by Prentiss-Hall Inc., 1975. The following United States patents on digital filters are also of interest for providing background information: U.S. Pat. No. 3,997,770 to Claasen et al; U.S. Pat. No. 4,034,196 to Butterweck et al; and U.S. Pat. No. 3,792,356 to Kobayashi et al.